A350566 - OEIS

%I #10 Aug 17 2023 08:16:42

%S 1,1,14,947,161388,56558003,36757837732

%N a(n) is the maximal permanent of an n X n matrix using the integers 1 to n^2.

%e a(2) = 14:

%e   [2, 3;

%e    4, 1]

%e .

%e a(3) = 947:

%e   [3, 7, 6;

%e    9, 4, 1;

%e    2, 5, 8]

%e .

%e a(4) = 161388:

%e   [ 2,  3, 16,  6;

%e    11, 13,  4, 10;

%e     8,  9,  5, 15;

%e    14, 12,  1,  7]

%e .

%e a(5) = 56558003:

%e   [10,  2, 19, 25,  3;

%e    11,  5, 23, 20,  8;

%e    21, 14, 12,  9, 15;

%e    13, 24,  6,  1, 18;

%e    16, 17,  7,  4, 22]

%e .

%e a(6) = 36757837732:

%e   [32, 30,  3, 19, 23,  2;

%e     1,  5, 34, 14, 11, 36;

%e    17, 18, 15, 31, 22, 16;

%e    29, 28,  7, 20, 24,  6;

%e    26, 25, 10, 21, 27,  9;

%e     4,  8, 35, 13, 12, 33]

%o (Python)

%o from itertools import permutations

%o from sympy import Matrix

%o def A350566(n): return 1 if n == 0 else max(Matrix(n,n,p).per() for p in permutations(range(1,n**2+1))) # _Chai Wah Wu_, Jan 21 2022

%Y Cf. A085000, A350565, A350858, A350859.

%K nonn,hard,more

%O 0,3

%A _Hugo Pfoertner_ at the suggestion of _Stefano Spezia_, Jan 21 2022